MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Today's Calculation Of Integral
2010 Today's Calculation Of Integral
654
Today's calculation of Integral 654
Today's calculation of Integral 654
Source:
October 7, 2010
calculus
integration
function
limit
calculus computations
Problem Statement
A function
f
(
x
)
f(x)
f
(
x
)
defined in
x
≥
0
x\geq 0
x
≥
0
satisfies
lim
x
→
∞
f
(
x
)
x
=
1
\lim_{x\to\infty} \frac{f(x)}{x}=1
lim
x
→
∞
x
f
(
x
)
=
1
.Find
∫
0
∞
{
f
(
x
)
−
f
′
(
x
)
}
e
−
x
d
x
\int_0^{\infty} \{f(x)-f'(x)\}e^{-x}dx
∫
0
∞
{
f
(
x
)
−
f
′
(
x
)}
e
−
x
d
x
.1997 Hokkaido University entrance exam/Science
Back to Problems
View on AoPS